NOAATR NESS 66
A UNITED STATES
NOAA Technical Report NESS 66
U.S. DEPARTMENT OF COMMERCE
National Oceanic and Atmospheric Administration
National Environmental Satellite Service
Effects of Aerosols on the Determination
of the Temperature of the Earth's Surface
From Radiance Measurements at 11.2 ^m
K. L. COULSON
,A TECHNICAL REPORTS
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ESSA Technical Reports
58 Angular Distribution of Solar Radiation Reflected From Clouds as Determined From TIROS IV Radi-
ometer Measurements. I. Ruff, R. Koffler, S. Fritz, J. S. Winston, and P. K. Rao, March 1967.
NESC 59 Motions in the Upper Troposphere as Revealed by Satellite Observed Cirrus Formations. H.
McClure Johnson, October 1966. (PB-173-996)
NESC 40 Cloud Measurements Using Aircraft Time-Lapse Photography. Linwood F. Whitney, Jr., and E. Paul
McClain, April 1967. (PB-174-728)
NESC 41 The SINAP Problem: Present Status and Future Prospects; Proceedings of a Conference Held at
the National Environmental Satellite Center, Suitland, Maryland, January 18-20, 1967. E. Paul
McClain, October 1967. (PB-176-570)
42 Operational Processing of Low Resolution Infrared (LRIR) Data From ESSA Satellites. Louis
Rubin, February 1968. (PB-178-123)
4 5 Atlas of World Maps of Long-Wave Radiation and Albedo--for Seasons and Months Based on Measure-
ments From TIROS IV and TIROS VII. J. S. Winston and V. Ray Taylor, September 1967. (PB-176-
44 Processing and Display Experiments Using Digitized ATS-1 Spin Scan Camera Data. M. B. Whitney,
R. C. Doolittle, and B. Goddard, April 1968. (PB-178-424)
5 The Nature of Intermediate-Scale Cloud Spirals. Linwood F. Whitney ,■ Jr . , and Leroy D. Herman,
May 1968. (AD-673-681)
NESC ithly and Seasonal Mean Global Charts of Brightness From ESSA 3 and ESSA 5 Digitized Pic-
tures, February 1967-February 1968. V. Ray Taylor and Jay S. Winston, November 1968. (PB-180-
nomial Representation of Carbon Dioxide and Water Vapor Transmission. William L. Smith,
.tistical Estimation of the Atmosphere's Geopotential Height Distribution From Satellite
nation Measurements. William L. Smith, February 1969. (PB-183-297)
optic/Dynamic Diagnosis of a Developing Low-Level Cyclone and Its Satellite-Viewed Cloud
Patterns. Harold J. Brodrick and E. Paul McClain, May 1969. (PB-184-612)
timating Maximum Wind Speed of Tropical Storms From High Resolution Infrared Data. L. F.
Ilub€ Timchalk, and S. Fritz, May 1969. (PB-184-611)
(Continued on inside back cover)
U.S. DEPARTMENT OF COMMERCE
Frederick B. Dent, Secretary
NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
Robert M. White, Administrator
NATIONAL ENVIRONMENTAL SATELLITE SERVICE
David S. Johnson, Director
NOAA Technical Report NESS 66
Effects of Aerosols on the Determination
of the Temperature of the Earth's Surface
From Radiance Measurements at 11.2 ^m
K. L. Coulson
.510 Atmospheric structure and composition
.42 Impurities and dust
.2 Terrestrial radiation
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402.
1. Introduction I
2. Atmospheric models 2
3. Radiative computations 4
4. Results of the calculations 8
A. Extinction and scattering by aerosols 8
B. Aerosol effects on temperature determinations 10
Digitized by the Internet Archive
EFFECTS OF AEROSOLS ON THE DETERMINATION OF THE TEMPERATURE OF
THE EARTH'S SURFACE FROM RADIANCE MEASUREMENTS AT I I .2 ym
National Environmental Satellite Service
Washington, D. C.
K. L. Cou I son
University of California
Davis, Ca I i fornia
ABSTRACT. The influence of atmospheric aerosols on out-
going terrestrial radiation in the window region at
11.2 ym is estimated by atmospheric modeling. Nine
different particle size distributions, 3 vertical aerosol
concentration profiles, and 5 vertical temperature profiles
are considered, for a total of 135 atmospheric models. For
each model, the upward radiant intensity was computed for
every 0.2 km from the surface to 20 km. From these values,
equivalent black-body temperatures were determined as a
function of height, and the error in the derived surface
temperature due to aerosols was computed. Results show
that absorption by aerosols is dominant over emission,
making the deduced surface temperature lower than actual,
except in the subarctic winter. Errors were generally
less than 2°K except under extreme conditions.
The influence that aerosols (atmospheric particulate matter) have on the
radiation emitted to space from the earth-atmosphere system has come under
increasing study in the past few years, particularly with regard to the
climatic changes that may be taking place as a result of the increase in the
pollution levels in our atmosphere. While such studies are of great value,
the radiative studies are also important in assessing the effects of aerosols
on the radiometric measurements made routinely from earth-orbiting satellites.
For example, vertical temperature profiles are deduced from radiometric
measurements made in several narrow spectral intervals in one or more atmos-
pheric absorption bands. However, these deductions require an accurate know-
ledge of the transmission properties of the atmosphere in those bands. While
the transmission trhough the principal atmospheric gases is accounted for,
the transmission through the aerosols is generally neglected. It is therefore
of interest to study how this neglect affects temperature determinations and
to learn how one can compensate for aerosol effects.
It was for these purposes that the present study was initiated. Although
emphasis will be on possible errors that may be produced in the surface
temperature by a neglect of the effects of aerosols, the results will be
applicable to certain other problems as well.
Recently, Stowe (1971) investigated absorption and scattering by aerosols
of radiation in the various spectral 'regions currently used for atmospheric
sounding. It was found that the intensity of the radiation scattered by the
aerosols is small compared to that emitted. Thus we assume that accuracy
will still be sufficient if scattering is neglected. Stowe used the "Haze M"
particle size distribution of Deirmendjian (1969) and the vertical profiles
of particle concentration obtained by Rosen (1967) and Elterman (1968). He
estimated that radiance determinations may be in error by as much as \5% in
the most transparent part (13.33 ym) of the 15 ym band of carbon dioxide
because of a neglect of absorption by aerosols. He also found that most of
the radiation absorbed from the upward stream is compensated for by radiation
emitted from the aerosol particles themselves, thereby reducing errors in
radiance estimates to generally less than \%. According to Stowe's analysis,
errors in the remote sensing of the temperature profiles are due to ( I ) large
underestimates of the atmospheric emission and (2) errors in the weighting
functions used for Inverting the radiometric measurements caused by a neglect
of the effects of atmosphertc aerosols.
In a recent study of aerosol effects in the natural atmosphere Mariatt
et al. (1971) measured atmospheric aerosol size distribution and sea surface
temperatures from altitudes ranging from 400 to 37,300 feet. Using the
measured aerosol concentrations and nearby radiosonde temperatures, he was
able to determine that for very hazy conditions with cloudless skies,
error in the computed blackbody temperature in the 8- to 14 ym window region
due to neglect of the observed aerosol absorption was of the order l°K.
For the present study we have focused our attention on estimating theoreti-
cal ly the effect of aerosols on the I I -ym window region. This region was
chosen to minimize the perturbing effects of absorption by atmospheric gases
and to estimate what accuracy of surface temperature determinations can be
reasonably expected from satellite measurements. The analysis can be readily
generalized to include other spectral regions.
2. ATMOSPHERIC MODELS
Calculations were made for a variety of model atmospheres. Since we were
chiefly interested in computing the difference in upward intensities when
aerosols were included and when aerosols were excluded, it was assumed that
the gaseous component of the atmosphere could be omitted from the models with-
out introducing serious errors. This is equivalent to the assumption that
the effect of the gases upon the emitted radiation is independent of the
effect of the aerosols, i.e., their combined effects are additive. Although
this is probably a poor assumption for many atmospheric absorption bands, it
should be a good one for the window region because of the weak molecular
absorption in that region.
Natural aerosols generally range in radius from 0.001 to 100 ym although
the greatest concentrations of the particles are generally between 0.1 and
10 ym. When there are dust storms, fog, or smog, the distribution is
changed somewhat by the addition of particles generally exceeding I ym in
size. Junge (1953) found that the observed size distribution could be
described reasonably well by the expression
d^ = C r
where N is the particle concentration, r is the particle radius, and C is a
proportionality constant. Later investigations by Junqe (1955) showed that
(I) could be generalized as
dN = C r" (2)
where v, generally known as the Junge distribution parameter, is only approx-
imately equal to 4. Variations of v from 4 occur as a result of humidity
changes, dust storms, or other variations in atmospheric phenomena.
To explore the influence of the particle size distributions on the
radiation transferred by the atmosphere, three values of v (3.5, 4.0, and
5.0) and three size ranges (0.08 to 10.0 ym, 0.06 to 5.0 ym, and 0.04 to
3.0 ym) were chosen since their scattering and extinction cross sections were
available (I. L. Zel'manovich and K. C. Shifrin, 1971).
To distinguish among clear, hazy, and very hazy atmospheres, vertical
profiles of aerosol number density based upon those of McClatchey et a I .
(1971) were used. These are shown in figure I, where the upper limit chosen
is an altitude of 20 km. The aerosol concentration above this level in their
— r ~ V
1 1 1 II II
i i i i ii| 1 — i i i i i ii| 1 — i i i i 1 1 1
(Sfc. Vis. -5 km|
/ VERY HAZY "
(Sfc. vis. =
\^^^,~-~~''(Sfc. Vis. = 1 km)
1 E^ iT^ ■ T-l-t^j 1 1
10 10 J 10 10
Particle Concentration (number per cm )
Figure I. — Vertical profiles of aerosol particle concentration for clear,
hazy, and very hazy atmospheric conditions.
models is too low to have any significant effect upon the radiation field.
For the clear and hazy atmospheres, the number density at the surface is such
that the surface visibi I ities for the case that 0.08 ^_ r <_ 10.0 ym and
v = 4.0 are 3 and 5 km, respectively. A model of a very hazy atmosphere was
constructed from that of the hazy atmosphere by arbitrarily extrapolating
the concentration of the hazy atmosphere at the I -km level to a surface value
corresponding to a visibility of I -km.
The models used for the aerosol distributions then were specified completely
by assuming that the relative size distributions were independent of altitude.
Bu combining the 9 relative size distributions with the 3 vertical concen-
tration profiles, we obtained 27 models of the aerosol distribution.
All that remains to be specified in the atmospheric models are the vertical
temperature profiles. Again, following McClatchey et al, (1971), we chose 5
profiles corresponding to mean conditions in the tropics and to the summer
and winter seasons for the mid latitudes and subarctic regions (fig. 2). Each
of the 5 temperature profiles were combined with each of the 27 aerosol
profiles to make a total of 135 model atmospheres for which computations were
3. RADIATIVE COMPUTATIONS
The scattering and extinction cross sections of the aerosols tabulated by
Zel'manovich and Shifrin were computed using the complex index of refraction
corresponding to that for water at a temperature of 20°C. The extinction
and scattering properties for the different aerosol models at a wavelength
Figure 2. — Vertical profiles of the mean temperature for the tropical region
and for the summer and winter seasons of the mid latitude and
A • 112/um, m = 1.133 - 0.124i
Extinction Cross Section
Scattering Cross Section
Albedo of Single Scattering
0.08 ^ r ^ 10.0
0.06 ± r i 5.0
0.04 i r ^ 3.0
0.08 i r ^ 10.0
. v 0.06 - r i 5.0
0.04 £ r i 3.0
Junge Distribution Paromet
Figure 3. — Extinction and scattering cross sections and the albedo of single
scattering vs. the Junge distribution parameter (v) for the
wavelength (A) and index of refraction (m) indicated. Size ranges
of the particles are given to the right of each curve.
equal to 11.2 ym can be seen from the plot of effective cross section
(extinction: o ex -\-; scattering; cr ex 4.) vs. the Junge exponent v (fig. 3). The
results have been normalized by dividing the effective cross section for the
aerosols by the total' number of particles assumed, which yields an effective
cross section of one particle which is radiatively typical of the total
aerosol model .
One of the basic parameters that characterize the transfer of radiation by
the aerosols is the extinction optical thickness t^ of a layer. This is
defined to be the property of a layer that causes unit radiation of wave-
length X normally incident upon it to be reduced to e~^X in passing through
the layer. It may be computed from a knowledge of the extinction cross
section of the aerosols and their vertical concentration profile by means of
t x (h)
where a, . is the normalized extinction cross section at the wavelength \
for a unit aerosoi concentration, N(Z) is the concentration as a function of
the altitude Z and h is the altitude of the top of the aerosol layer. The
cross sections given by Zel'manovich and Shifrin and the vertical concentra-
tion profiles shown in fig. I were used in eq. (3) to compute the optical
thickness as a function of the altitude for all 27 aerosol models. Table I
TABLE I. — Optical thickness of model aerosol atmospheres
r ( m)
r ( m)
shows the resulting optical thickness for the models for the layer extending
from the surface to the 20*-km level.
From the variation of the optical thickness with altitude, the transmissi-
vity from any level in the model to any other level could be readily computed
By restricting the study to a narrow spectral interval and assuming that
scattering is small compared to absorption (a reasonable assumption for most
of the aerosol models) one can approximate the transmiss ivity in the vertical
from the altitude Z| to the altitude Z? by the expression
(Z „ZJ = e
-Jt x (Z^ - t x (Z j) sec 6
X v " I
where t x (Z ( ,Z 2 ) is the transmiss ivity, t x (Zj) and t x (Z 2 ) are the optical
thicknesses from the surface to the levels Z| and Z 2 , respectively, and 9 is
the angle between the direction of the radiation and the vertical. For the
present study, the radiation was considered only in the vertical direction,
in which case sec 9 = 1.0.
The intensity of radiation at any altitude h may be computed from the
l x (h)
e A B A ( W°
,h> + j b a (t(Z)J
d T (Z,h)
where I, (h) is the intensity of the upward radiance at the altitude h,
B^(T) is the blackbody radiance at the temperature T, T is the surface
temperature, t^(Z,h) is the transmissiyity from the altitude Z to the
altitude h, e^ is the surface emissivity, and x is wavelength. Since the
temperature and transmissi vi ty are given at a finite number of levels, (5)
was replaced by the approximate expression;
m*0 j H5 L ( a m+ |- i x m' I
where Z represents the altitude of the £-f- h level and e^ has been set to
unity for all model atmospheres.
The equivalent blackbody temperature, T , that corresponds to the radiant
intensity IMZ ) is defined by the expression,
Bx'V = ^V ' (7)
Comparing this with the surface temperature T , the temperature error AT
is defined by the relation
AT = T - T
This quantity, which is of primary interest in the study, represents the
error in the determination of the temperature from a measurement of the
radiance at some altitude above the surface. In the absence of any aerosol
or molecular components to the atmosphere, T eq = T Q and therefore AT = 0.
With aerosols and air molecules in the atmosphere, T ^ T , due to the
r eq o'
absorption and emission that takes place in the atmosphere.
The transport of radiation through the model atmospheres was computed and
analyzed by means of eqs. (4) to (8). The procedure used was:
(1) Compute the optical thickness as a function of altitude for every
0.2 km from the surface to an altitude of 20 km for each of the 27
aerosol models using (3).
(2) Determine the transmissivi ties between each of the levels for each
aerosol model using (4).
(3) Compute the intensity of radiation directed vertically upward at
each level for each aerosol model and for each of the 5 temperature
profiles (135 model atmospheres) using (6).
(4) Calculate the equivalent blackbody temperature T QQ from the upward
radiation intensity values by means of (7).
(5) Determine the temperature errors by (8), using T as determined
from the radiance values and T as assumed in the atmospheric
4. RESULTS OF THE CALCULATIONS
A. Extinction and Scattering by Aerosols
The general extinction and scattering characteristics of the different
aerosol models can be seen in the curves of effective cross section (fig. 3).
The effective cross section corresponds to that for a single effective
particle representative of each distribution.
The curves for the extinction cross section a ex f show there is a relatively
strong dependence of extinction cross section on the range of the radii taken
into account. For instance, cr ex f for 0.08 _< r <_ 10.0 um is about an order of
magnitude greater than that for 0.04 <^ r <_ 3.0 um, and the ratio between
these extinction cross sections is practically independent of v. Physically,
an increase of the minimum size from 0.04 to 0.8 ym effectively eliminates
many small particles from consideration, since the Junge distribution contains
many small particles. Conversely, an increase of the upper size limit does
not add many particles, but those added are very effective attenuators. The
net result, as the size limits for the radii increase, is an increase in the
size of the average particle of the distribution and an increase in the value
of the extinction cross section.
The same reasons ing can be applied to the curves of the scattering cross
section, a sea -f.. However, for a given value of v, the rate of increase of
°scat w '+ n increase in the limits of the radii is greater than that for o ex f.
This can be explained with the aid of figure 4 in which the extinction and
scattering efficiency factors (Q ex f =a ext^ 7rr ^ anc ' ^scat =a ext / 7Tr ^) are
plotted versus the particle radius r for three different values of the complex
index of refraction (Q ex + > Qscat^ • While the real part of the index of re-
fraction is the same for all three cases, the imaginary part differs. The
index for the middle curve of each set is the same as that used in obtaining
the results of figure 3. By comparing the curves in figure 4 with the super-
imposed straight lines that have geometric slopes equal to I and 4, it can be
concluded that a sca ^/i\r^ * r^ and Cg^/frr^ ^ r for all but the largest values
of the particle radius. Then, cr sca -j- ^ r° and tf ex -|- ^ r^ for sufficiently small
values of r. The scattering cross section, therefore, is particularly
sensitive to the sizes of the scattering particles, and anything that changes
the average size of the distribution has more effect on c sca -f- than on cr ex -j-.
This property is responsible for the large spread of the curves of figure 3
for the three size ranges.
The dependence of the scattering and extinction cross sections on the radius
also explains the decrease in the value of the cross sections with increase in
the Junge exponent v. By increasing the magnitude of v, a steeper negative
slope is given to the distribution. This increases the number of small
particles at the expense of the large ones and therefore decreases the size of
the average particle causing the cross sections to decrease. Again, because
of the greater sensitivity of a , to particle size than <j -., the curves for
— i — i — i i i 1 1 1 1 1 — i i i i 1 1 1 1 — i — n
Index of Refraction
>// / ft
Particle Radius (^.m)
j i i '''I'
Figure 4. — Extinction and scattering efficiency factors Q(=a/irr ) versus the
radius r for the wavelength A and index of refraction (m)
Solid lines that have geometric slopes of I and 4 are superimposed
for the purpose of comparison.
a scat decrease more rapidly with increasing v than the curves for (Text* For
instance, in figure 3 the curve for the middle size range shows a decrease
in a S cat by a factor of 180 from v = 3.5 to v = 5.0, but a decrease of only
12.5 for a ex+i
Since the total attenuation is produced by a combination of absorption and
scattering, we can write for the respective cross sections the relation
a ext a abs a scat
By dividing by cr ex ^- we obtain the quantity
CT scat q abs
which is designated the albedo of single scattering, w. Physically, it
represents the part of the total attenuation that is contributed by scatter-
ing. Then the quantity
■ - _ c?abs
represents the part due to absorption. Curves of u" for the various aerosol
models are plotted, according to the scale given on the right, as the bottom
family in figure 3. It is striking that such a small fraction of the total
attenuation is due to scattering. The curves show that the contribution of
scattering to the extinction is generally between I % and 10 % of the total.
Only for particles in the size range 0.08 _f_ r <_ 10.0 ym and v = 4.0 is
w > 10/6, and It gets as low as 0.2 % in the size range 0.04 ± r <_ 3.0 ym.
There are two consequences of the existence of such smal I values of U for
the present problem. First, absorptivity of the aerosol particles is high,
which means if Kirchhoff;s law is assumed valued for aerosols, that their
emissivity is likewise high. Thus, most of the energy subtracted from a beam
of radiation traversing the aerosol medium is absorbed by the aerosol
particles, but their high emissivity ensures that they also lose energy
efficiently by remitting the radiation. In fact, if the particles were at
the same temperature as the source from which they were receiving radiation
(the surface in this problem), they would maintain radiative equilibrium and
would undergo no temperature change. This does not necessarily mean, however,
that the same amount of radiation would be returned to the original beam, as
the angular dependence of the absorbed and emitted radiation may not be the
The second result of the high absorptivity of the aerosol particles is that
the single scattering assumption is a good approximation of reality. Because
of single scattering the radiative field is weak; the series attributable to
secondary and higher order scattering of already scattered radiation
converges rapidly. If 10 % is due to primary scattering, only I % would be
due to secondary scattering,- 0.10 % to tertiary scattering, etc. Thus, any
errors caused by neglect of multiple scattering would be minor compared to
those of the unknown physical validity of the models.
The relatively strong decrease of to with increasing v and the close spacing
of the three curves of nr shown in figure 3 both indicate the high absorptivity
of small particles in comparison with that of large particles. As pointed
out above, cr sca -f- ^ r& and a ex f ^ r- 5 for smal I particles. Since cr ex f is
dominated by o a ^ s , one can also write o a ^ s *v r^. Thus, as particle size
decreases, Q sca f decreases about I0- 5 times as fast as a bs> thus producing
the result shown.
B. Aerosol Effects on Temperature Determinations
Using the atmospheric models discussed above, computations have been made
for determining the error that would be produced by various aerosol distri-
butions in the intervening atmosphere in surface temperature determinations
from satellite altitude. The temperature error AT is defined here as the
difference between the actual temperature, i.e., that assumed to exist at the
surface, and the equivalent blackbody temperature which would be deduced from
measurements of the upward radiance at the top of the atmosphere. Thus a
positive value of AT indicates the actual temperature exceeds that measured,
and vice versa.
The temperature errors determined by this procedure are plotted as a function
of the Junge distribution parameter v for the five models of atmospheric
temperature profile in figures 5 to 9. In each case, computations of AT have
been made for three different intervals of particle size and for clear, hazy,
and very hazy atmospheric conditions.
Results for the tropical atmosphere are shown in figure 5. The curves are
defined by three points each, the points corresponding to v 3.5, 4.0, and
5.0. As would be expected from the results shown previosuly in figure 3, the
largest temperature errors are for the largest aerosol size range
(0.08 <_ r _< 10.0 urn), for v = 3.0, and for the very hazy atmosphere. For this
worst case AT approaches 2.0°K.
Just how realistic this worst case is for actual atmospheric conditions is
hard to say. We do not know enough about the aerosols that exist in the
atmosphere, particularly in the tropical atmosphere, to make a firm judgment.
However, the very hazy atmospheric model, with its low horizontal visibility,
does not occur freq uently in the tropics. The clear model is probably more
applicable for tropical atmospheres, and AT for the worst clear case is only
about l°K. If the Junge distribution parameter v has a more moderate value
of 4.0, as has been found to be the case in many instances, then AT for the
clear tropical atmosphere is only about 0.25°K.
Throughout the computations, it is shown that AT is very sensitive to the
range of particle sizes assumed. The magnitude of AT decreases by a factor
of about 10 as the size range assumed decreases from 0.08 < r <_ 10.0 ym to
0.04 <_ r <_ 3.0 ym. This means that the error comes within the noise of
measurements for the smaller size range, but that the result of aerosols of
\i 0.08 ^ r
" \ \
"~^~^^ — *
' — ■•
3 5 4.0 4 5 5 3 5 4 4 5 5 3 5
Junge Distribution Parometer - y
Figure 5. — Temperature error AT versus the Junge distribution parameter v for
a tropical atmosphere for three degrees of haziness and the
particle size ranges indicated. The wavelength is 11.2 ym.
; 0.08 £ r £ lO.O^m
40 45 50 35 40 4.5 50 35 4.0 4.5 5.0
Junge Distribution Parameter - y
Figure 6. — Same as figure 5, mid- latitude summer.
2.0| — — i — — i — — i | 1 1 f
0.04 ^ r ^ 3.0// m
_ 0.06 ^ r ^ 5.0/* r
\ 0.08 -r
50 3.5 4.0 4.5 5.0 3.5
Junge Distribution Parameter - if
Figure 7. — Same as figure 5, mid-latitude winter.
^ r ^ 5.0/um
\ 0.08 ^ r
4.5 5.0 35 40 45 50 3.5
Junge Distribution Parameter -
Figure 8. — Same as figure 5, subarctic summer.
r - 5.0// m
5.0 3.5 40 4.5 5.0 3.5 4.0
Junae Distribution Parometer - 1/
Figure 9. —Same as figure 5, subarctic winter.
the larger size range is a serious limitation for cases requiring precise
determinations of the surface temperature.
Comparable statements can be made about the temperature errors for other
atmospheric models, as shown in figures 6 to 9. In general, the magnitude
of the errors decreases with increasing latitude, and the errors are smaller
in winter than in summer for a given location and aerosol model. The reason
for the trend toward smaller values of AT with decreasing surface temperature
is not that the radiative fluxes are smaller, but that the lapse rates are
more stable and the tropopause tends to occur at a lower level at the higher
latitudes. Thus there is less difference between the temperatures of the
aerosols and the surface at the middle and higher latitudes than in the
tropics. In fact, the temperature inversion in the subarctic winter model
causes T to be very small for that case (fig. 9) and the order of the curves
is reversed so that AT decreases with increasing haziness of the atmosphere.
The mechanism responsible for the reversal can be seen in figure 14.
The data are segregated according to the haziness of the model In figures
10 to 12. For the clear case (fig. 10), only for the largest size range and
v < 4.0 does AT exceed 0.5°K, it is generally 0.2°K or less. As mentioned
before, AT generally increases with increasing haziness and reaches nearly
2.0°K for the worst conditions in a very hazy atmosphere (fig. 12). Only for
the subarctic winter is increasing haziness accompanied by a decreasing
magnitude of AT (compare figs. 10, II, and 12).
The results so far have been for radiation emerging to space from the top
of the atmosphere, but it is instructive to see what part of the atmosphere
contributes most to AT. This feature is shown for the tropical atmosphere
by the plot of AT vs. altitude in figure 13. The curves for all three size
ranges exhibit the same general characteristics; only the magnitude of the
temperature errors are different. Most of the error is produced in the highly
concentrated aerosols near the surface. Above an altitude of about 4 km, the
contributions to AT are all about the same for a given range of aerosol sizes.
These characteristics are not unexpected, when the vertical profiles of
aerosol concentrations are considered (fig. I). Only in the lowest levels of
the atmosphere do the concentrations differ significantly among the models,
so the primary differences in AT among them should occur in the lowest levels.
At the higher altitudes the aerosol concentrations do not differ significantly
for the models chosen, a fact which is responsible for the similar slopes of
the curves above about 4 km.
Figure 14 shows that the vertical profiles of AT for the mid latitude and
subarctic summer models are qualitatively similar to those for the tropical
model atmosphere, althoughthe magnitudes are somewhat different. In all of
these cases most of the temperature error is introduced in the lowest layers
of the atmosphere. In the subarctic winter model, on the other hand, a small
negative value of AT is introduced in the lowest levels, with Its magnitude
increasing as the haziness of the atmosphere increases. This reversal of
sign is produced by the temperature inversion in the low levels of the sub-
arctic winter temperature profile. Aerosol particles in the region from the
surface to about 2 km altitude are at a temperature higher than that of the
surface, and as a consequence add more radiation into the upward stream by
emission than they subtract by absorption. Above the inversion, a greater
0.04 ^ r £ 3.0/im
0.0 a?a ** tt w
r ^ 10.0/i
^ i * iii ^^.
3.5 4.0 4.5 5.0 3.5 4.0 4.5 50 3.5 4.0
Junge Distribution Parameter - V
Figure 10. — Temperature error AT vs, the Junge distribution parameter v for
a clear atmosphere for five atmospheric temperature profiles and
the particle size ranges indicated. The wavelength is 11.2 ym.
-\ 1 1 i 1 r
0.04 £ r £ S.OyUi
\ 0.08 ^
35 40 45 5.0 3.5 4.0 4.5 5.0 3.5 4.0
Junge Distribution Parameter — V
Figure II. — Same as figure 10, hazy atmospnere.
i 1 r
0.04 = r £ 3.0yu
m °- 8 - r -
- \ V
5 40 45 50 3.5 40 4.5 5.0 35 40 45 5.0
Junge Distribution Parameter — y
Figure 12. — Same as figure 10, very hazy atmosphere.
Tropical, if = 4.0
04 £ r £ 3.0p m 0.06 ^ r ^ 5.0// m 0.08 ^ r ^ 10.0^ m
00 02 0.4 0.6 0.0 0.2 0.4 06 0.0 0.2 0.4 0.6
Temperature Error (°K)
Figure 1 3. —Temperature error AT vs. altitude for a tropical atmosphere for
three degress of haziness, a single value of the distribution
parameter v, and particle size ranges indicates. The wavelength
is I I .2 ym.
1/ =4.0, 0.08=r = 10.0/jim
i W '
i i | ii ;
j ' I 1 /; I
1 1 H
1 Very j 1 ! ;
Hazy ; I i ;
1 1 I ! ;
1 1 1 :
j i !/■
i : 1 ' :
' I- 1
1 i :/
i ill -
1 it; Tropical
'I J L
■ \ ■ ;
l l| Summer
1 if Mid LfltitM' 4 "
I 1 !!
i / ; i
1 1 I :
1 :f Summer
| if Mid-Latitude
i / ':
* / * ;
t Subarctic /
f i i
>** i i
-0.2 0.0 0.2 0.4 0.6-0.2 0.0 0.2 0.4 0.6-0 2 2 4 6
Temperature Error (°K)
Figure 14. — Temperature error AT vs. altitude for the size range
.08 < r < 10.0 ym and the Junge distribution parameter v = 4.0
for 3 degreees of haziness and 5 temperature profiles indicated.
absorption than emission of energy by the particles causes the curves for
the subarctic winter model to assume the same general character as that of
the other models, but the negative values have to be compensated for by
colder layers before the errors become positive. This results both in very
small final errors of AT for the subarctic winter atmosphere, and in a de-
crease of error with increasing haziness in contrast to the other cases. By
a small increase of the temperature inversion in the model, the temperature
error could be completely erased or reversed in sign for the subarctic winter
atmosphere. Such an inversion is not at all unusual in subarctic or arctic
regions, although it apparently does not occur as a mean condition.
The figures were drafted by Robert Ryan, the manuscript was typed by
Betty Loveless, and Paul Pellegrino computed and graphed most of the results.
Dei rmendj fan, D., Electromagnetic Scattering on Spherical Polyd i spersions ,
American Elsevier Publishing Co., Inc., New York, N. Y., 1969, 290 pp.
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im Spurenstoff hausha 1 1 der Troposphare, " Tel I us , 5, 1953, pp. 1-26.
"The size distribution and aging of natural aerosols as determined from
electrical and optical data on the atmosphere," Journal of Meteorology , 12,
1955, pp. 13-25.
Marlatt, W. E., Cole, H. I., Harlan, J. C, and Hjermstad, J. I., "Infrared
radiation transfer through atmospheric haze layers," Final Report , NAS
5-1 1631, Atmospheric I imiations to remote sensing, Department of Watershed
Science, Colorado State University, Fort Collins, Colo., 1971, 62 pp.
McClatchey, R. A., Fenn, R. W., Selby, J. E. A., Volz, F. E., and Garing, J. S.,
"Optical properties of the atmosphere (revised)". Environmental research
papers , No. 354, AFCRL-7 1-0279, Optical Physics Laboratory, Air Force
Cambridge Research Laboratories, Bedford, Mass., 1971, 85 pp.
Rosen, James M., "Simu I taneous dust and ozone soundings over North and
Central America", University of Minnesota-Atmospheric Physfcs-25, Report
Stowe, Larry L., Jr., "The effects of particulate matter on the radiance of
terrestrial infrared radiation", Institute of Geophysics and Planetary
Physics, University of California, Los Angeles, 1971, 109 pp.
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Leningrad, U.S.S.R., Hydrometeorolog ica I Office, 1971, 167 pp.
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